Descripción: In this paper we study the optimization problem for the first eigenvalue of the p-Laplacian plus a potential V with respect to V, when the potential is restricted to a bounded, closed and convex Bet of Lq(Ω).

Descripción: A comprehensive study of nonstoichiometry titanium oxide thin films (TiO x , 0.3≤x≤2) prepared by ion beam deposition technique is reported. The physical properties of the material are studied by ultraviolet and x-ray photoelectron, Raman, and Fourier transform infrared spectroscopies, and atomic force microscopy. An abrupt transition from metallic characteristics to a wide gap semiconductor is observed in a very narrow range of oxygen variation. Concomitantly with this change the crystal structure and morphology suffer remarkable physical properties modifications. This transformation is ascribed to surface-volume energy minimization due to the influence of oxygen determining the size of the TiO 2 particles during coalescence. © 2010 American Institute of Physics.

Descripción: We consider the optimization problem of minimizing ∫Ω G (| ∇ u |) + λ χ{u > 0} d x in the class of functions W1, G (Ω) with u - φ0 ∈ W01, G (Ω), for a given φ0 ≥ 0 and bounded. W1, G (Ω) is the class of weakly differentiable functions with ∫Ω G (| ∇ u |) d x < ∞. The conditions on the function G allow for a different behavior at 0 and at ∞. We prove that every solution u is locally Lipschitz continuous, that it is a solution to a free boundary problem and that the free boundary, Ω ∩ ∂ {u > 0}, is a regular surface. Also, we introduce the notion of weak solution to the free boundary problem solved by the minimizers and prove the Lipschitz regularity of the weak solutions and the C1, α regularity of their free boundaries near "flat" free boundary points. © 2008 Elsevier Inc. All rights reserved.

Descripción: Context. A magnetic cloud (MC) is a magnetic flux rope in the solar wind (SW), which, at 1 AU, is observed ∼2-5 days after its expulsion from the Sun. The associated solar eruption is observed as a coronal mass ejection (CME).Aims. Both the in situ observations of plasma velocity distribution and the increase in their size with solar distance demonstrate that MCs are strongly expanding structures. The aim of this work is to find the main causes of this expansion and to derive a model to explain the plasma velocity profiles typically observed inside MCs.Methods. We model the flux rope evolution as a series of force-free field states with two extreme limits: (a) ideal magneto-hydrodynamics (MHD) and (b) minimization of the magnetic energy with conserved magnetic helicity. We consider cylindrical flux ropes to reduce the problem to the integration of ordinary differential equations. This allows us to explore a wide variety of magnetic fields at a broad range of distances to the Sun.Results. We demonstrate that the rapid decrease in the total SW pressure with solar distance is the main driver of the flux-rope radial expansion. Other effects, such as the internal over-pressure, the radial distribution, and the amount of twist within the flux rope have a much weaker influence on the expansion. We demonstrate that any force-free flux rope will have a self-similar expansion if its total boundary pressure evolves as the inverse of its length to the fourth power. With the total pressure gradient observed in the SW, the radial expansion of flux ropes is close to self-similar with a nearly linear radial velocity profile across the flux rope, as observed. Moreover, we show that the expansion rate is proportional to the radius and to the global velocity away from the Sun.Conclusions. The simple and universal law found for the radial expansion of flux ropes in the SW predicts the typical size, magnetic structure, and radial velocity of MCs at various solar distances. © 2009 ESO.